Using optical sensors to assess the impact of infrequent sampling on the uncertainty of stream annual mean turbidity and total phosphorus concentrations, and how this can affect the water quality status 

Using optical sensors to assess the impact of infrequent sampling on the uncertainty of stream annual mean turbidity and total phosphorus concentrations, and how this can affect the water quality status | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Using optical sensors to assess the impact of infrequent sampling on the uncertainty of stream annual mean turbidity and total phosphorus concentrations, and how this can affect the water quality status Eva Skarbøvik, Anastasija Isidorova, Maria Kämäri, Pasi Valkama, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6436252/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The annual mean concentration of nutrients is a commonly used parameter in implementing the Water Framework Directive, to assess current environmental status and distance from the environmental goal. However, the concentration of nutrients in streams may vary significantly over short time spans so finding the ‘true mean’ concentration can be difficult. We used hourly turbidity data from optical sensors in 10 streams in four Nordic countries, and we prepared mimic data series for weekly, fortnightly, and monthly sampling strategies. We calibrated the sensor turbidity data with the total phosphorus data from grab samples. We then assessed how the annual mean values of both turbidity and phosphorus can vary, depending not only on the number of samples collected per year but also on stream and catchment characteristics. We found that the uncertainty of the annual mean concentration of total phosphorus decreased with increasing sampling frequency and increasing catchment size, and with a decreasing proportion of agricultural land in the catchment. We also found that there was a higher risk of underestimating the mean TP than of overestimating it, meaning that managers will assume that water quality is better than it is. Our work has resulted in an initial model that calculates the number of samples needed to achieve a given uncertainty in annual mean TP concentration for streams of varying catchment size and land use. Water quality streams turbidity sensor phosphorus uncertainty Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction Several studies have focused on the uncertainty in using infrequent water grab sampling to estimate loads of different constituents in streams (Koskiaho et al., 2010 ; Marttila & Kløve, 2010 ; Cassidy & Jordan, 2011 ; Bieroza et al., 2014 ; Villa et al., 2019 ; Leigh et al., 2019 ). Less attention has been given to the uncertainty in calculating the annual arithmetic mean of stream water concentration of different substances, although this parameter has become increasingly important with the introduction of the EU Water Framework Directive (WFD, EC, 2000 ). The mean annual concentrations of nutrients such as phosphorus (P) and nitrogen (N) have been given threshold levels in different types of water bodies in geographical intercalibration exercises in European countries (EC, 2008 ; Birk et al., 2012 , 2013 ; Poikane et al., 2019 ), resulting in five ecological status groups (high, good, moderate, poor, and very poor) where the environmental goal is the good/moderate boundary. Furthermore, mean concentrations of nutrients have been correlated to biological quality elements to develop indices of ecological status in both streams and lakes (Lyche Solheim et al., 2008, 2025 ). Examples from streams include benthic algae and total phosphorus (TP) (Schneider & Lindstrøm, 2012; Schneider & Skarbøvik, 2022 ); diatoms and TP (Kahlert et al., 2023 ); and macroinvertebrates and organic pollution, including TP (Friberg et al., 2010 ). From this, it follows that arithmetic mean nutrient concentrations are used to assess the state of the water body and thereby the extent of environmental mitigation measures needed to reach the environmental goal (Balana et al., 2011 ; Carvalho et al., 2019 ), as well as to assess if the implemented measures have functioned as planned (Lyche-Solheim et al., 2008 ; Bol et al., 2018 ). Reliable estimates of mean nutrient concentrations are important not only environmentally but also economically. If an environmental goal is too strict, more mitigation measures may be implemented than necessary, whereas goals that are too slack could mean the water bodies in question becoming increasingly eutrophic. Excessive eutrophication can result in blooms of blue-green algae, which again can increase the cost of drinking water purification and jeopardize the tourism industry and recreational activities (Gourevitch et al., 2021 ; Juutinen et al., 2022 ; Immerzeel et al., 2023 ). A decade ago, the total cost of mitigating the eutrophication of the Baltic Sea was estimated at EUR 2,800 million per year (BalticSTERN, 2013). Pretty et al. ( 2003 ) estimated that the cost of damage from freshwater eutrophication in England and Wales amounted to USD 105 − 160 million per year. Of this, the cost of addressing eutrophication was estimated at about USD 77 million per year, in addition to costs associated with drinking water treatment, the reduced value of waterfront properties, and business losses in recreation and tourism. While this illustrates the importance of the annual arithmetic mean concentration of a substance for water management, it is a well-known fact that the concentration of substances in streams can vary dramatically over short periods of time (e.g. Vercruysse et al., 2017 ). Hence, the question arises of how often water samples should be collected to find a reliable mean concentration, and whether this might differ among stream types. Brauer et al. ( 2009 ) found that in small headwater streams the number of samples required per month to obtain mean seasonal (April/May–September/October) concentrations within an error of 20% varied from 2 to 25 for turbidity, 2 to 39 for total phosphorus, and 1 to 16 for total nitrogen, corresponding to a maximum of 300, 468, and 192 annual samples respectively. In a larger river (5,500 km 2 ), Skarbøvik et al. ( 2012 ) used suspended particulate matter (SPM) data collected twice a day over five years and found that the reliability of seasonal mean SS concentrations improved with increased sampling frequency, but even weekly samples could give errors of up to 70% in seasons with high sediment loads. McDowell et al. ( 2024 ) calculated the statistical power of data from streams monitored monthly in New Zealand. Based on long-term data over a period of 20 years, more than 95% of all monitored sites had sufficient power and samples to detect changes in nutrients, but to detect changes within a five-year period would have required a fivefold increase in the sampling frequency for dissolved reactive phosphorus. Skeffington et al. ( 2015 ) studied dissolved phosphorus, dissolved oxygen, pH, and water temperature in four English streams for the purpose of assessing how uncertain the mean annual concentrations would be for classification according to the WFD. They found that the effect of sampling frequency on the classification of the water body depended on how close the range of concentrations was to the WFD class boundaries. In some cases, monthly sampling for a year could result in the same water body being assigned to three or four different WFD classes with 95% confidence, whereas with weekly sampling the mean concentration could result in the water body being assigned to one or two classes. In the most extreme case, however, the same water body could have been assigned to any of the five WFD quality classes, clearly demonstrating the risk involved in using this water management system. At the same time, many monitoring programmes in Europe are still based on samples collected fortnightly, monthly, or even less often (Webb et al., 1997 ; Skarbøvik et al., 2014 ; Axe et al., 2022 ). This is linked to economic considerations, since water sampling and laboratory analyses can both be costly. An ability to study the variation of concentrations in rivers in more detail has been acquired through the development of sensor technology (Rode et al., 2016 ; Rozemeijer et al., 2025 ). Sensor monitoring of turbidity, for example, offers frequent datasets at a relatively low cost. Turbidity is a water quality parameter related to the opaqueness (cloudiness) of water and has been used as a substitute for, amongst others, SPM and TP (Stubblefield et al., 2007 ; Ruegner et al., 2013 ; Bieroza & Heathwaite, 2015 ; Skarbøvik & Roseth, 2015; Lannergård et al., 2019 märi et al., 2020 ; Skarbøvik et al. 2023 ). The main purpose of this study has been to assess the uncertainty in estimating annual mean turbidity and annual mean TP concentration based on six different sampling strategies that are often applied in national or regional monitoring programmes and using data from 10 Nordic streams. Furthermore, we have aimed to investigate whether the uncertainty levels in mean concentration can be explained by easily available characteristics of the streams and their catchments, so that authorities can use this knowledge when they plan for cost-effective sampling in streams. Methods The study is based on 10 existing in-situ sensor stream turbidity data series and grab samples from monitoring programmes financed by different funding sources. The methods used are similar apart from some small variations as described below, the details of which are in the supplementary material. Case studies Ten streams in four countries were selected on the basis of their having in-situ turbidity sensor monitoring and water sampling data for TP to be used for calibration. We were aiming to find three years of data from each stream, preferably including a dry year, a wet year, and a hydrologically average year, but in this selection, we also favoured data series with the fewest possible data gaps. The cases represent a variety of catchment sizes, land use distributions, predominant soil types, turbidity ranges, and WFD environmental goals (Table 1 [1] ). The area-specific water discharge (over the long term and for the three selected years) is shown in Table 2. Further characteristics of the streams and their catchments are given in the supplementary material (Table S-VIII). Table 1 Case streams’ catchment areas, main land uses, WFD river types, classification boundaries, and main soil types. Further stream and catchment characteristics are given in the supplementary material (Table S-VIII) Country Stream name Catchment area Land use (%) WFD river type WFD environmental goals for TP (µg TP/l) Main soil types 4 km 2 Agric Forest Other All are lowland rivers Reference condition High/ Good Good/ Moderate Median/ Poor Poor/ Very Poor DK Horndrup 5.48 70 19 11 RCB-5 1 106 3 Sandy loam (98.8%), Organic/Peat (1.2%) DK Lyby-Grønning 11.3 84 2 14 RCB-5 1 106 3 Sandy loam (47%), Clayey loam (52%) FI Aurajoki 756 37 51 12 Clay river, medium <40 40 60 100 130 Morain (54%), clay-rich (28%), organic/peat (11%) FI Hirvijoki 148 23 72 5 Clay river, medium <40 40 60 100 130 Clay (51%), Coarse sand with clay (25%), Gyttja/peat (10%), Coarse sand (6%), Fine sand (5%) FI Lepsämänjoki 22 37 53 10 Clay river, small <40 40 60 100 130 Clay (63 %), Coarse sand with clay 9%, Gyttja/peat 8% Coarse sand 6%, Fine sand with clay 6%, Fine sand 6% NO Mørdre 7.7 65 28 7 Clay river, small 50 Silty clay (65%), ca. 35% morain in upstream parts NO Skuterud 4.5 61 29 10 Clay river, small 80 Silty clay (60%), ca 40% morain in upstream parts SE Hågaån 121 31 55 14 R-07 2 30 43 61 101 152 Morain (33%), clay (23%) SE Skivarp 122 77 9 9 R-07 2 22 32 45 75 112 Clay (47%), sandy soils (27%) SE Sävjaån 746 34 57 9 R-07 2 27 38 53 89 133 Morain (41%) clay (24 %) 1 RCB-5: Lowland, Large, moderate-high alkalinity. 2 R-07: Lowland, < 10 000, organic and calcareous. (Lowland ( 1 mekv/l) and humic (>30 mgPt/l).). May be transferred to a new typology class, Clay rivers, but this has not yet been done. 3 The mean of a span of 68-136 µg TP/l. The boundary is based on Lyche Solheim et al. (2024) https://projects.au.dk/fileadmin/projects/nordbalt-ecosafe/Filer/D1_2_FactSheetsWithRefValuesAndGMboundaryValuesDraft.pdf since DK has not yet set class boundaries for streams. 4 For larger streams, the soil type close to the monitoring station is given Table 2 Average area-specific water discharge (l/s and km 2 ) for the selected years and longer term means (LTM). Blue, green, and pink indicate the wettest, average, and driest of the three chosen years C Name 2016 2017 2018 2019 2020 2021 2022 2023 LTM Years for LTM - l/s/km 2 - From-to DK Horndrup 10.0 8.6 8.2 9.2 1991-2020 DK Lyby 7.0 3.6 3.9 5.2 1991-2020 Fi Aurajoki 4.9 12.0 9.2 9.4 1994-24 FI Hirvijoki 6.0 15.0 13.1 12.9 2017-22 FI Lepsämänjoki 7.4 11.5 15.6 10.4 2006-2024 NO Mørdre 12.6 8.2 3.5 8.4 1991-2020 NO Skuterud 24.7 12.0 10.9 14.4 1991-2020 SE Hagaån 9.2 4.5 14.5 7.6 1991-2020 SE Skivarp 7.5 5.5 7.4 6.4 1991-2020 SE Sävjaån 2.6 3.9 6.1 7.6 1991-2020 Sensor equipment and sensor data quality control An overview of the sensor brands used is given in the supplementary material (Table S-I). Data were quality-controlled by the respective institutes according to their standard procedures. This included a control to assess whether outliers could be explained by a rapid increase in water discharge or by pollution on the sensor lens. The respective institutes also assessed whether cleaning the lenses affected the data, usually seen as an abrupt change in turbidity after cleaning. Missing values were linearly interpolated using the R package ‘chillR function interpolate_gaps’ (Luedeling, 2018). Missing values were interpolated if the number of consecutive gaps did not exceed 48, which equals two days of measurements. Longer gaps were not interpolated and were left as missing values. Water sampling procedures and chemical analyses of TP for calibration In all the streams, a surrogate relationship equation between sensor turbidity and the TP water sample data have been calculated. TP samples were collected by hand, by automatic samplers, or by both. There were variations in the sampling strategies of the monitoring programmes (supplementary material, Table S-II), but all had at least 65 TP samples for calibration (supplementary material, Table S-III). In a comparison of 31 streams in Northern Europe, Skarbøvik et al. (2023) found that at least 70 samples for calibration yielded an R 2 value above 0.6 between turbidity and SS. The TP was analysed by accredited laboratories according to nationally approved standards (supplementary material, Table S-IV). Data analyses and statistics Mimic data series were prepared for all streams by extracting different frequency data from the hourly sensor turbidity data. We assumed monitoring regimes where sampling can occur randomly within the boundaries of a week, 14 days, or a month. In addition, we also assumed a more realistic sampling strategy, selecting Mondays–Thursdays during working hours, due to the practical need to deliver samples to the laboratory by Thursday before closing hours. This resulted in the following six sampling strategies: using all hours of the day every weekday and selecting (i) weekly, (ii) fortnightly, and (iii) monthly samples from this; and using only working hours (8:00–15:00) from Monday to Thursday and selecting (iv) weekly, (v) fortnightly, and (vi) monthly sampling from this. For each sampling strategy, 1,000 datasets were randomly constructed, and annual mean concentrations were calculated. These were then compared with annual mean concentrations based on hourly data from the sensors. This enabled us to calculate the percentage of uncertainty for each sampling strategy by using the ChillR package. Total uncertainty was then calculated as the root mean square error (RMSE) of prediction divided by the actual mean turbidity value from hourly observations (TrueTurb): RMSE/TrueTurb. Next, we decided on a set of potential factors to explain any variation in total uncertainty between the streams. The factors were chosen based on typical information that is readily available. This included catchment size and land use, as well as area-specific discharge and flashiness of the flow. For the latter, the Richards-Baker flashiness Index (RBI; Baker et al., 2007) was calculated using the ContDataQC in R package (Leppo, 2022). In addition, we included three characteristics related to turbidity: standard deviation, proportion of outliers, and range. For range, the lower values for all streams were zero or near zero, and we hence tested for the maximum turbidity recorded and the 95 and 98 percentiles. Since the maximum turbidity in some cases can equal the maximum value that the sensor can record, and is often reached in only a few spikes that may have been caused by instrument error, we decided that using the 95 and 98 percentiles would be more robust. We then fitted a linear model using the R program and checked this for multicollinearity by using variance inflation factors (VIF) and normality of residual distribution (Shapiro test and residual plots). Some of the parameters were log10-transformed to improve the visual representation in the graphs (area, discharge per unit area, and percentiles of turbidity). While the total dataset comprised 90 observations (10 rivers, 3 years, 3 sampling strategies – here omitting the sampling only during working hours, see results’ section), the model was developed using a randomly selected half (45 observations) and validated with the remaining half (45 observations). This we did four times to ensure that the random selection did not include outliers or other data that affected the results. For all the streams, the TP concentrations analysed from grab samples were used for calibration between turbidity and TP. No rule has been determined for how good such a correlation should be in order to use turbidity as a proxy for another substance. In this study, we both assessed the R 2 and scrutinized the correlation graphs (supplementary material) and decided that an R 2 of 0.6 or above gave an acceptable correlation. This issue is further deliberated upon in the discussion session, but it should be noted that most of the data analyses have been performed on turbidity alone, and not on the proxy. Results Importance of sampling strategy for calculating mean turbidity The variations in the mean annual turbidity for all 10 streams for (relatively) dry, average, and wet years are shown in the supplementary material (supplementary material, Figure S-II). The smallest and most extreme variations in turbidity values were found, respectively, in the dry year of 2018 in the Finnish river Aurajoki and in the wet year of 2020 in Denmark’s Horndrup Stream. The river Aurajoki’s range in mean annual turbidity was 13–41 FNU (standard deviation of 3.6), whereas the Horndrup Stream had a range of 6–133 FNU (standard deviation of 15). Figure 1 combines the total uncertainty of mean annual turbidity (y-axis) for all three years in the 10 streams based on the six sampling strategies (x-axis). As expected, the uncertainty in mean annual turbidity increased with decreased sampling frequency. There was a slight difference between sampling at any random hour and on weekdays and sampling during working hours on Monday to Thursday, as the median uncertainty was lower when the sampling was limited to working hours (Fig 1). This illustrates how the shorter the window of sampling opportunity, the lower the mean value may be, as more extreme events are likely to be missed. However, when compared to the differences between monthly, fortnightly, and weekly sampling, the differences between sampling on all days and at all hours of the day versus sampling only on four days a week during working hours were deemed negligible. For all streams in total, weekly sampling (on all days at all hours) gave a mean uncertainty of true mean turbidity of 17±9% (mean ± standard deviation with a range of 4.5%-35% (max. and min.)), fortnightly sampling – 26±13% (10% – 51%) and monthly sampling 40±19% (16%–85%). Uncertainty varied among the studied streams (Figure 2). The highest levels of uncertainty were found in the two Danish streams and the lowest were found in the three Finnish streams and the Swedish Hagaån. There was no clear connection between annual water discharge and the uncertainty of finding annual true mean turbidity, as shown for weekly sampling in Figure 3. Six of the streams had their highest level of uncertainty in the wettest year, whereas four streams had their highest level of uncertainty in years of either dry or average water discharge. However, in the Swedish Skivarp, there was little difference in water discharge between the wet and average years. The results indicate that, for some streams, the uncertainty of finding average annual concentrations can increase in years with high water discharge, but that most probably the distribution of water discharge throughout the year is also of importance. Our data material was not deemed sufficient to explore more detailed analyses of the hydrological impact on uncertainty beyond looking at the flashiness index, which also had a poor correlation with the uncertainty (Table 3). Factors affecting uncertainty To evaluate which factors may cause the variation in uncertainty of the mean annual turbidity, we tested against a set of available, possible explanatory factors (Table 3, and supplementary material, Figure S-I). We found correlations between total uncertainty and land use percentage of agricultural (R 2 =0.43) or forested (R 2 =0.39) land, catchment size (R 2 =0.35), and sampling frequency (R 2 =0.31). We then fitted these parameters into a multiple linear model to explore how the parameters together could predict total uncertainty. As noted above, the dataset of 90 observations was split in two, and the model was calibrated for 45 datasets and then tested on the remaining 45. Table 3 Relationship between the total uncertainty (of finding mean annual turbidity), and a set of available explanatory factors Possible explanatory factors (x in the equations in the next column). All were log10 transformed Equation (y is the total uncertainty; x is the tested explanatory factor) R 2 p Stats. Info 1 Number of samples per year (n) y=10^(x*-0.00935+1.64153) 0.31 1.42E-08 NND Size of catchment area (km 2 ) y=10^(x*-0.20221+1.70088) 0.35 9.76E-10 ND Proportion of agricultural area (%) y=10^(x*0.00881+0.90449) 0.43 1.63E-12 ND Proportion of forested area (%) y=10^(x*-0.00788+1.65694) 0.39 3.41E-11 ND Discharge per catchment area (l/s and km 2 ) y=10^(x*0.01506+1.3574) 0 0.5 NS Flashiness index (RBI) y=10^(x*0.38044+1.24591) 0.07 1.25E-02 ND Turbidity 98-percentile (NTU/FNU) y=10^(x*0.26894+0.77781) 0.12 6.65E-04 ND Turbidity maximum level (NTU/FNU) y=10^(x*0.33404+0.42717) 0.25 6.98E-07 ND Turbidity 95-percentile (NTU/FNU) y=10^(x*0.16224+1.04445) 0.03 0.08 NS Ratio of turbidity outliers/number of samples y=10^(x*0.45126+0.04556) 0.08 7.45E-03 ND The standard deviation of turbidity (NTU/FNU) y=10^(x*0.34252+0.8062) 0.20 1.07E-05 ND 1 Statistical information: NND: Not normally distributed; ND: Normally distributed; NS: Not significant Some parameters were omitted due to having a similar nature or strong correlation with others (e.g. percentage of agriculture was negatively correlated with percentage of forest, the 95 and 98 percentiles of turbidity were correlated, and so on). The VIF scores of the parameters used were below 5 for all predictions, indicating no multicollinearity concern. The model included the following parameters: number of samples (n) catchment size (Cz) percentage of agricultural area (A) discharge per area (Qa) flashiness of water discharge (RBI) 98 percentile of turbidity (T) The fitted regression of this uncertainty model is as follows: U= 10^[1,3914 - (0.0084 * n) – (0.1019 * log10(Cz)) + (0.0052 * A) – (0.0895 * log10(Qa)) + (0.0644 * log10(T))] Eq. 1 (Model 1) where U is the total uncertainty of finding true mean turbidity. The model was significant, p<0.001, indicating that at least one of the predictors significantly affected the total uncertainty. The model explained 75% of the variance in the total uncertainty (adjusted R 2 =75). See supplementary material Table S-V for further details. Next, we tested a much simpler model (Model 2), which includes only the parameters n, Cz, and A. These were chosen because they are easily available parameters and, moreover, the other parameters in Model 1 seemed less important (cf. p-values in Table 3). The simplified uncertainty model is expressed as: U = 10^[1.3812 – (0.0095 * n) – (0.0003* Cz) + (0.0066* A)] Eq. 2 (Model 2) The model was significant, p<0.001, indicating that at least one of the predictors significantly affected the total uncertainty. The model explained 79% of the variance in the total uncertainty (adjusted R 2 =79). See supplementary material Table S-VI for further details. Figure 4 shows the results of the tests for both models. Based on Equation 2, we simulated how uncertainty can change when the number of samples collected per year from the streams included in this study is increased (Figure 5a for catchment size and 5b for land use). Table 4 shows the number of samples per year that are needed to find a mean turbidity value with uncertainty less than 10%, 20%, and 40% respectively. In terms of land use, we have shown this for the proportion of agricultural land, but in the 10 studied catchments, the remaining land use was mostly forest (Table 1), which indicates that an increasing proportion of forest will reduce uncertainty. The table illustrates, for example, that larger rivers may be sampled less often than smaller streams within the same uncertainty, but at the same time, a large agricultural river may need the same number of samples as a smaller forested stream. A large river (800 km 2 catchment area) with only 20% agriculture could give a mean TP concentration within 10% uncertainty with 29 samples per year, whereas a small stream (5 km 2 catchment area) with 85% agriculture would need 100 samples to achieve the same level of uncertainty. Table 4 The number of samples each year to keep within 10%, 20% and 40% uncertainty (U) of finding ‘true mean’ concentration of turbidity, based on catchment area (Cz) and proportion of agricultural land (A). Empty cells: data from our study did not cover this range No of samples a year to keep within a % of uncertainty (U) Cz (km 2 ) A (%) 10% U 20% U 40% U 800 20 29 - - 50 49 18 - 85 74 42 10 150 20 49 18 - 50 70 39 7 85 95 63 31 5 20 54 22 - 50 75 43 11 85 100 68 36 Correlations and significance for phosphorus concentrations in streams In the above results, the data analyses are concerned with turbidity, as we wanted to assess the uncertainty in finding annual means independently of what turbidity may be a proxy for. However, turbidity is not used to evaluate the state of water bodies under the WFD. We therefore correlated turbidity with TP and found that three of the 10 streams had a correlation (R 2 ) below 0.6 (supplementary material, Table S-V and Figure S-III) – the Skivarp, Hagaån, and Mørdre – and these three streams have therefore been omitted from the following data analyses. The reasons for the poorer correlations may be linked to phosphorus from sources such as sewage or animal manure, but this issue will not be further explored in this work. An important question arising from the above data analyses is whether the annual mean TP concentration is more likely to be underestimated or overestimated. Hence, we have used the data for the seven streams with an acceptable TP–turbidity correlation and estimated that, on average for 1,000 runs, there was a larger risk of underestimating the mean turbidity and, hence, the TP mean concentration. The proportion of runs where estimated mean turbidity was lower than the ‘real mean’, was, on average, 58% for weekly sampling, 60% for fortnightly sampling, and 65% for monthly sampling (Figure 6). From this, it follows that managers will most likely assume that the state of a river water body is in a better class than it is, based on a ‘true mean’ of hourly sampling. Next, we compared the calculated sensor-based annual means of TP with the environmental goals for all streams (Figure 7) for weekly and monthly sampling strategies. For monthly sampling, the span between the lowest and highest annual mean TP concentrations varied from 86 µg/l in the Swedish Sävjaån to 978 µg/l in the Danish Lyby, and the average for all streams was ca. 300 µg/l. Weekly sampling gave a span of 6 µg/l for Sävjaån, 350 µg/l for Lyby, and an average range of 117 µg/l for all streams. In some of the streams, the lowest mean sensor-based TP concentration was higher than the environmental goal. This included Aurajoki and Skuterud for both the weekly and monthly sampling strategies, and Lyby, Hirvijoki, and Lepsämänjoki for the weekly sampling strategy. This means that whatever sampling strategy is used for the three years with different hydrological conditions, the annual mean concentration of TP would show the stream as having a moderate or worse status. For the other streams, the lowest and highest estimates of the mean TP concentrations could fall below, above, or close to the environmental goal. Discussion Although the WFD was agreed by EU member states 25 years ago (in 2000 in the EU and in 2006 in Norway), there are still issues to be further explored related to its cost-effective implementation (Carvalho et al., 2019 ; Lyche-Solheim et al., 2025). The economic costs of implementing the WFD may become an increasing challenge in a world facing uncertain economic developments due to ongoing military conflicts and potential trade wars, and a subsequent need to intensify food production locally. Moreover, eutrophication is a challenge that can be expected to increase in magnitude in the years to come due to climate change (Kosten et al., 2012 ; Jeppesen et al., 2015 ; Solheim et al., 2025). Hence, it will be of great importance to choose the most cost-effective monitoring strategy to ensure that streams under the WFD are properly managed. In this study, our main concern has been to assess the uncertainty of using the mean concentration of TP as an indicator of ecological status in streams. Achieving accurate estimates of TP concentrations in streams is also of great importance for the ecological quality of lakes as riverine inputs often determines the in-lake concentration (Jensen et al., 2006 ). In our study of 10 Nordic streams, we found that the average mean turbidity, which is a parameter that correlates both with TP and other particle-associated substances, will depend on several factors, for which we extracted three explanatory variables that are easily available and can therefore provide a basis for planning cost-effective monitoring strategies by managers: catchment size, catchment land use, and the number of samples collected per year. Importantly for managers, we found that larger streams can be sampled less often than smaller streams within the same uncertainty, but at the same time, a large agricultural river may need the same number of samples as a smaller forested stream. Our model is based on a series of assumptions that are discussed further below. Our model indicates that larger streams tend to have less temporal variation in turbidity and, therefore, also in concentrations of particle-associated substances than do smaller streams, which often respond more rapidly to rain or snow melt events, with ensuing increases in water flow. Similar results were found by Coynel et al. (2004) when comparing the uncertainty of flux estimates of suspended particulate matter. They concluded that to find SS fluxes within 20% uncertainty, the large river Garonne would need to be sampled every third day, whereas a smaller river would have to be sampled as often as every seventh hour. Our model also indicates that the uncertainty of a mean annual concentration is higher in agricultural catchments than in catchments dominated by forest cover. De Wit et al. (2020) documented that observed TP concentrations in Nordic agricultural streams were much higher than in forested and natural catchments. As discussed by Skarbøvik et al. ( 2023 ), the soil types in Nordic catchments dominated by agriculture are likely to be more fine-grained than in catchments dominated by forest, and that seasonal changes in vegetation cover leave the soil more vulnerable to erosion. There may also be fewer trees along the riverbanks and therefore more bank erosion in agricultural areas (Beeson & Doyle, 1995 ; Abernethy & Rutherfurd, 2000 ). This, again, can result in higher concentrations and thereby greater variations in the concentrations of particulate matter and TP, thereby making it more difficult to find the true mean concentration. The use of the model in other stream types needs to be tested on new datasets, but as we have based our model on 10 streams of differing size and land use, we expect our model to be relatively robust, at least for streams with characteristics similar to those of our Nordic streams (Table 1 , Table 2 , and Table S-VIII in supplementary material). The implications of our findings for managers following up the WFD include designing monitoring strategies based on catchment size and land use. However, as also noted by Skeffington et al. ( 2015 ), the need for accurate estimates of the status of the water body may increase as the water quality approaches the environmental goal. In streams where the environmental goal will not be reached regardless of sampling strategy (Fig. 7 ), fine-tuning to find a less uncertain annual mean TP concentration may not be the most sensible use of funds and a better strategy may be to use available funds to reduce the loss of phosphorus and sediments to the water environment. On the other hand, a less accurate monitoring strategy would make it more difficult to track whether implemented measures work as planned. Another question is how these findings may affect the many biological indices that are based on annual mean TP concentrations. We have shown that the mean turbidity value found from monthly, fortnightly, and even weekly sampling in streams will most likely, in about 60% of the runs, be lower than the ‘true mean’ (Fig. 6 ). This also implies that the indices developed between TP and biological indicators are probably calibrated with TP concentrations that are too low, since the biological indicators are based on monitoring programmes that usually use intervals far less frequent than hourly intervals (e.g. Schneider & Skarbøvik, 2022 ). On the other hand, our true mean includes all of a year’s peak values that have been detected at hourly intervals. Certainly, for both hazardous substances and the calculation of loads of all substances, the identification of maximum concentrations will be important. But does it follow that the same is true for the mean concentration of nutrients? In other words, will a shorter period of high concentrations of nutrients seriously affect biota, or is the ‘true mean’, in terms of effect on biological indicators, more related to the TP concentrations outside of the peaks? This is a question worth pursuing in forthcoming studies. The source of errors in the data used in this study relates mainly to the reliability of the sensors used and to the relationship between turbidity and proxies (here: TP concentration). Kahiluoto et al. ( 2019 ) found that turbidity sensor measurement had an uncertainty of 11–27% (k = 2) for the range of 5–40 FNU. Skarbøvik et al. ( 2023 ) discussed how different sensor brands may give different slopes of the correlation between SPM and turbidity by sensors, but they also found that this could be related to the type of filter used when analysing SPM. As far as we know, there is no set rule for how good a correlation should be in order to use turbidity as a proxy for another substance. Lannergård et al. ( 2019 ) presented an overview of the R 2 s between TP and turbidity from eight different studies, varying from 0.25 to 0.90, but where most of the correlations had an R 2 above 0.6. Minaudo et al. ( 2017 ) have shown that a nonlinear model between turbidity and TP can sometimes be more feasible than a linear regression model. Moreover, Kämäri et al. ( 2020 ) studied the correlations between turbidity from sensors and TP from grab samples in three Finnish streams. The R 2 values of the linear calibration varied between 0.77 and 0.80, but if a few high TP concentrations were omitted, the R 2 was reduced to 0.57–0.74. This illustrates that R 2 alone is insufficient evidence for correlations, and that consideration should be given to correlation graphs to check for single high values, as well as to other statistics. In our case, this was achieved through the graphs shown in the supplementary material, Figure S-III, and when analysing impacts of sampling frequency on TP annual means, we only used the rivers with an R 2 between turbidity and TP above 0.65. Our study has shown that stream water quality monitoring programmes with infrequent sampling run a high risk of obtaining unreliable mean concentrations. McDowell et al. ( 2024 ) noted that in a river monitoring network in New Zealand with monthly sampling, costs would have to increase by 5.3 times to reach statistically acceptable results within a 5-year period. They therefore concluded that it might be necessary to increase monitoring investments in order to demonstrate policy results for water quality improvement. Moreover, as stated by the EC ( 2003 ): The cost of measures for improvement in water status would be orders of magnitude greater than the costs of monitoring. The extra costs of monitoring to reduce the risk of misclassification might therefore be justified in terms of ensuring that decisions to spend larger sums of money required for improvements are based on reliable information on status. Nevertheless, in practice there will often be a trade-off between costs for monitoring and costs for measures, and the distance between the environmental goal and the current state of a water body may offer guidance on how detailed a monitoring programme should be. For water bodies that are in a very poor state, monitoring could perhaps be geared towards finding the main pollutant sources and funding might best be used to reduce the impact of these. Conclusions The uncertainty in annual mean turbidity and TP concentrations increased with decreased sampling frequency in 10 Nordic streams. Weekly samples gave the lowest uncertainty, whereas uncertainty increased with fortnightly and monthly sampling. Uncertainty varied with stream and catchment properties, but for all streams there was a higher risk of underestimating the mean TP than of overestimating it. This means that there is a risk that managers will believe their water bodies are in a better state than they actually are. In our simpler model, the variation in uncertainty was explained by catchment size and land use in the catchment. We found that large streams may be sampled less often than smaller streams, but at the same time, a large agricultural river may need the same number of samples as a smaller forested stream. A large river with a catchment area of about 800 km 2 and with only 20% agriculture could give a mean TP concentration within 10% uncertainty with 29 samples per year, whereas a small stream with a catchment area of 5 km 2 and 85% agriculture would require 100 samples a year to achieve the same level of uncertainty. By using our model, managers could direct their monitoring programmes towards the optimal sampling frequency for rivers of different catchment size and land use. At the same time, they might look at the distance between the environmental goal and the current status, as funding could be better spent on reducing nutrient losses if the water bodies are in a particularly poor state. Declarations All authors have read, understood, and have complied as applicable with the statement on “Ethical responsibilities of Authors” as found in the Instructions for Authors. Funding declaration : This paper was funded by the EU Horizon project NORDBALT-ECOSAFE (Grant Agreement No. 101060020). The Danish work was also funded by Innovation Fund Denmark from the Industrial Researcher programme for the project ‘SENTEM’ at Envidan and Aarhus University, Denmark (Grant Agreement No. 0153-44 00078B). The Finnish data was funded by the Centre for Southwest Finland Economic Development, Transport and the Environment (sensor data from the Aurajoki River) and The Water Protection Association of The River Vantaa (sensor data from the River Lepsämänjoki). Parts of the Finnish work has also been funded by the Flagship Program granted by the Research Council of Finland for Digital Waters Flagship (decision no. 359250). The Norwegian data were supported by the Biowater Centre of Excellence, funded by NordForsk under Project No. 82263, and the Norwegian Research Council under Contract No. 342631/L10, as well as from the JOVA Program, funded by the Norwegian Ministry of Agriculture and Food. The Swedish data was funded by the Swedish Agency for Marine and Water Management and by the EU-Life IP project Rich Waters. Author Contribution E.S. wrote the main manuscript text and had the idea for the paper. A.I. prepared many of the figures and tables, performed the statistical analyses and contributed with text.M.K., P.V., S.G.M.vV, E.E.L., J.F. contributed with data, inputs to the tables, ideas, and text. B.K. contributed with text, ideas and advice. References Abernethy, B & Rutherfurd, I.D. 2000. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6436252","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":455912812,"identity":"95594e2d-16eb-42b2-afe9-990c8739c022","order_by":0,"name":"Eva Skarbøvik","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIie3QPQrCMBiA4ZSAWSJdK3iIzyl00asUCl11FBRUCk45QAXxDl0Et4RAu+QAHRwUwbluHY0/a6TdHPIQSPjghSQIOc7fEgiB2eR6jijgbonumnib7efwkx/EF6/R4ykjfCR3h/OQESzwbG5PBlkCmFZxeOIaZH680zDtRTjT9gS0MJevMUCVRPJ6VBTMwv2tPZnosvaaevVN9i0SIBwQrZRJYiHzdYskKPlMUV1CyJWQWaHebzETe+KnJL82xQIY2aQPvlQT5it5oz9+7EW0mDiO4zidPAHBiVXRlk/R+wAAAABJRU5ErkJggg==","orcid":"","institution":"Norwegian Institute of Bioeconomy Research (NIBIO)","correspondingAuthor":true,"prefix":"","firstName":"Eva","middleName":"","lastName":"Skarbøvik","suffix":""},{"id":455912813,"identity":"afb9a424-6459-4108-a90f-212a196a38d3","order_by":1,"name":"Anastasija Isidorova","email":"","orcid":"","institution":"Norwegian Institute of Bioeconomy Research (NIBIO)","correspondingAuthor":false,"prefix":"","firstName":"Anastasija","middleName":"","lastName":"Isidorova","suffix":""},{"id":455912814,"identity":"6d750162-efa2-4f96-8a3c-1b342a88b6ad","order_by":2,"name":"Maria Kämäri","email":"","orcid":"","institution":"Finnish Environment Institute (Syke)","correspondingAuthor":false,"prefix":"","firstName":"Maria","middleName":"","lastName":"Kämäri","suffix":""},{"id":455912815,"identity":"f74937bb-8587-4b82-a7b3-adce55e5853c","order_by":3,"name":"Pasi Valkama","email":"","orcid":"","institution":"Finnish Environment Institute (Syke)","correspondingAuthor":false,"prefix":"","firstName":"Pasi","middleName":"","lastName":"Valkama","suffix":""},{"id":455912816,"identity":"dde1e861-aa99-4bbb-ae47-bb9946a47f9c","order_by":4,"name":"Sofie G.M. van't Veen","email":"","orcid":"","institution":"Aarhus University","correspondingAuthor":false,"prefix":"","firstName":"Sofie","middleName":"G.M. van't","lastName":"Veen","suffix":""},{"id":455912817,"identity":"cdf4f1fa-6517-47e9-bb3f-865a6cb60b72","order_by":5,"name":"Emma E. Lannergård","email":"","orcid":"","institution":"Swedish University of Agricultural Sciences","correspondingAuthor":false,"prefix":"","firstName":"Emma","middleName":"E.","lastName":"Lannergård","suffix":""},{"id":455912818,"identity":"cf734008-3e56-4b2c-9682-8acf1ccbafa4","order_by":6,"name":"Jens Fölster","email":"","orcid":"","institution":"Swedish University of Agricultural Sciences","correspondingAuthor":false,"prefix":"","firstName":"Jens","middleName":"","lastName":"Fölster","suffix":""},{"id":455912819,"identity":"14ab4a03-72ca-4100-b6ce-0a697be45921","order_by":7,"name":"Brian Kronvang","email":"","orcid":"","institution":"Aarhus University","correspondingAuthor":false,"prefix":"","firstName":"Brian","middleName":"","lastName":"Kronvang","suffix":""}],"badges":[],"createdAt":"2025-04-12 19:38:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6436252/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6436252/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82716654,"identity":"21bae411-a031-45b7-ad48-d0472f34b244","added_by":"auto","created_at":"2025-05-14 12:21:20","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":37395,"visible":true,"origin":"","legend":"\u003cp\u003eUncertainty in the calculation of annual mean turbidity as a function of the sampling strategy combined for all samples, all streams, and all years (the grey boxes show the standard deviation, the horizontal line within the grey boxes represents the median value, and the vertical dashed lines show the maximum and minimum values)\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6436252/v1/875709324be66f43b07de664.jpeg"},{"id":82717491,"identity":"17b1e1c6-ee38-48e3-8f73-536d6f8491f7","added_by":"auto","created_at":"2025-05-14 12:29:20","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":76688,"visible":true,"origin":"","legend":"\u003cp\u003eUncertainty of calculating annual mean turbidity in the ten rivers for three years each (the red, blue, and green dots represent monthly, fortnightly, and weekly sampling respectively, on all weekdays and at all hours of the day)\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6436252/v1/1a46790b44a389318f031920.jpeg"},{"id":82718064,"identity":"09f4add7-df79-494a-974d-8821ee1e7fb7","added_by":"auto","created_at":"2025-05-14 12:37:20","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":179671,"visible":true,"origin":"","legend":"\u003cp\u003eOn the basis of weekly sampling, the graph shows the total uncertainty (of finding the true mean turbidity) for three years (green triangles) with differing water discharge (bars, Q, shown as l/s/km\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6436252/v1/ee4e917850d26c4632c96636.jpeg"},{"id":82717496,"identity":"7acb72f9-e955-4206-a6b2-38f10f18eb34","added_by":"auto","created_at":"2025-05-14 12:29:20","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":165740,"visible":true,"origin":"","legend":"\u003cp\u003ePredicted vs actual values in Model 1 (left-hand chart) and the simpler Model 2 (right-hand chart) for the 45 observations not used in the modelling; dashed line is the 1:1 line\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6436252/v1/624ce48d7c2dd576a6e1fb4e.jpeg"},{"id":82716653,"identity":"c529a2c3-eab1-4e8c-9210-42b80a02acbe","added_by":"auto","created_at":"2025-05-14 12:21:20","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":57818,"visible":true,"origin":"","legend":"\u003cp\u003eUncertainty as a function of the number of samples per year (n) based on Model 2. (a) shows variations with catchment size and (b) variations with the proportion of agricultural land\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6436252/v1/d8a5526fa0ef4e4aeddaafb0.jpg"},{"id":82716655,"identity":"f760934d-6721-4938-b809-3ba49b7ca25e","added_by":"auto","created_at":"2025-05-14 12:21:20","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":34464,"visible":true,"origin":"","legend":"\u003cp\u003ePercentage of 1,000 runs where estimated mean turbidity was less than the ‘true’ mean turbidity; sampling strategies include monthly, fortnightly, and weekly, on all weekdays at all hours of the day\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6436252/v1/932f730f59801e16ae6384d9.jpg"},{"id":82719094,"identity":"741e0386-4f64-457c-8ebc-31567ad38f6d","added_by":"auto","created_at":"2025-05-14 12:45:20","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":67908,"visible":true,"origin":"","legend":"\u003cp\u003eEnvironmental goals (green horizontal lines) compared to average TP concentrations (µg/l) as derived from turbidity data from three years for each stream, for weekly and monthly sampling on all days and at all hours\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6436252/v1/516227563933526712e1fc87.jpg"},{"id":84985453,"identity":"bd850aa9-8c50-464f-8809-814db71a6ade","added_by":"auto","created_at":"2025-06-19 14:17:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1473279,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6436252/v1/88db9c39-2674-478c-81ce-440cbe849de2.pdf"},{"id":82718066,"identity":"b0532228-d648-404a-82d8-5caad5a749bb","added_by":"auto","created_at":"2025-05-14 12:37:20","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1514702,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementarymaterials.docx","url":"https://assets-eu.researchsquare.com/files/rs-6436252/v1/479493d2acfe7c2766ea3922.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Using optical sensors to assess the impact of infrequent sampling on the uncertainty of stream annual mean turbidity and total phosphorus concentrations, and how this can affect the water quality status ","fulltext":[{"header":"Introduction","content":"\u003cp\u003eSeveral studies have focused on the uncertainty in using infrequent water grab sampling to estimate loads of different constituents in streams (Koskiaho et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Marttila \u0026amp; Kl\u0026oslash;ve, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Cassidy \u0026amp; Jordan, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Bieroza et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Villa et al., \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Leigh et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Less attention has been given to the uncertainty in calculating the annual arithmetic mean of stream water \u003cem\u003econcentration\u003c/em\u003e of different substances, although this parameter has become increasingly important with the introduction of the EU Water Framework Directive (WFD, EC, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). The mean annual concentrations of nutrients such as phosphorus (P) and nitrogen (N) have been given threshold levels in different types of water bodies in geographical intercalibration exercises in European countries (EC, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Birk et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2012\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Poikane et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), resulting in five ecological status groups (high, good, moderate, poor, and very poor) where the environmental goal is the good/moderate boundary. Furthermore, mean concentrations of nutrients have been correlated to biological quality elements to develop indices of ecological status in both streams and lakes (Lyche Solheim et al., 2008, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Examples from streams include benthic algae and total phosphorus (TP) (Schneider \u0026amp; Lindstr\u0026oslash;m, 2012; Schneider \u0026amp; Skarb\u0026oslash;vik, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e); diatoms and TP (Kahlert et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2023\u003c/span\u003e); and macroinvertebrates and organic pollution, including TP (Friberg et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). From this, it follows that arithmetic mean nutrient concentrations are used to assess the state of the water body and thereby the extent of environmental mitigation measures needed to reach the environmental goal (Balana et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Carvalho et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), as well as to assess if the implemented measures have functioned as planned (Lyche-Solheim et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Bol et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eReliable estimates of mean nutrient concentrations are important not only environmentally but also economically. If an environmental goal is too strict, more mitigation measures may be implemented than necessary, whereas goals that are too slack could mean the water bodies in question becoming increasingly eutrophic. Excessive eutrophication can result in blooms of blue-green algae, which again can increase the cost of drinking water purification and jeopardize the tourism industry and recreational activities (Gourevitch et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Juutinen et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Immerzeel et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). A decade ago, the total cost of mitigating the eutrophication of the Baltic Sea was estimated at EUR 2,800\u0026nbsp;million per year (BalticSTERN, 2013). Pretty et al. (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2003\u003c/span\u003e) estimated that the cost of damage from freshwater eutrophication in England and Wales amounted to USD 105\u0026thinsp;\u0026minus;\u0026thinsp;160\u0026nbsp;million per year. Of this, the cost of addressing eutrophication was estimated at about USD 77\u0026nbsp;million per year, in addition to costs associated with drinking water treatment, the reduced value of waterfront properties, and business losses in recreation and tourism.\u003c/p\u003e \u003cp\u003eWhile this illustrates the importance of the annual arithmetic mean concentration of a substance for water management, it is a well-known fact that the concentration of substances in streams can vary dramatically over short periods of time (e.g. Vercruysse et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Hence, the question arises of how often water samples should be collected to find a reliable mean concentration, and whether this might differ among stream types. Brauer et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) found that in small headwater streams the number of samples required \u003cem\u003eper month\u003c/em\u003e to obtain mean seasonal (April/May\u0026ndash;September/October) concentrations within an error of 20% varied from 2 to 25 for turbidity, 2 to 39 for total phosphorus, and 1 to 16 for total nitrogen, corresponding to a maximum of 300, 468, and 192 annual samples respectively. In a larger river (5,500 km\u003csup\u003e2\u003c/sup\u003e), Skarb\u0026oslash;vik et al. (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) used suspended particulate matter (SPM) data collected twice a day over five years and found that the reliability of seasonal mean SS concentrations improved with increased sampling frequency, but even weekly samples could give errors of up to 70% in seasons with high sediment loads. McDowell et al. (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) calculated the statistical power of data from streams monitored monthly in New Zealand. Based on long-term data over a period of 20 years, more than 95% of all monitored sites had sufficient power and samples to detect changes in nutrients, but to detect changes within a five-year period would have required a fivefold increase in the sampling frequency for dissolved reactive phosphorus. Skeffington et al. (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) studied dissolved phosphorus, dissolved oxygen, pH, and water temperature in four English streams for the purpose of assessing how uncertain the mean annual concentrations would be for classification according to the WFD. They found that the effect of sampling frequency on the classification of the water body depended on how close the range of concentrations was to the WFD class boundaries. In some cases, monthly sampling for a year could result in the same water body being assigned to three or four different WFD classes with 95% confidence, whereas with weekly sampling the mean concentration could result in the water body being assigned to one or two classes. In the most extreme case, however, the same water body could have been assigned to any of the five WFD quality classes, clearly demonstrating the risk involved in using this water management system.\u003c/p\u003e \u003cp\u003eAt the same time, many monitoring programmes in Europe are still based on samples collected fortnightly, monthly, or even less often (Webb et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Skarb\u0026oslash;vik et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Axe et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). This is linked to economic considerations, since water sampling and laboratory analyses can both be costly. An ability to study the variation of concentrations in rivers in more detail has been acquired through the development of sensor technology (Rode et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Rozemeijer et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Sensor monitoring of turbidity, for example, offers frequent datasets at a relatively low cost. Turbidity is a water quality parameter related to the opaqueness (cloudiness) of water and has been used as a substitute for, amongst others, SPM and TP (Stubblefield et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Ruegner et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Bieroza \u0026amp; Heathwaite, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Skarb\u0026oslash;vik \u0026amp; Roseth, 2015; Lannerg\u0026aring;rd et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003em\u0026auml;ri et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Skarb\u0026oslash;vik et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe main purpose of this study has been to assess the uncertainty in estimating annual mean turbidity and annual mean TP concentration based on six different sampling strategies that are often applied in national or regional monitoring programmes and using data from 10 Nordic streams. Furthermore, we have aimed to investigate whether the uncertainty levels in mean concentration can be explained by easily available characteristics of the streams and their catchments, so that authorities can use this knowledge when they plan for cost-effective sampling in streams.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eThe study is based on 10 existing in-situ sensor stream turbidity data series and grab samples from monitoring programmes financed by different funding sources. The methods used are similar apart from some small variations as described below, the details of which are in the supplementary material.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eCase studies\u003c/p\u003e\n\u003cp\u003eTen streams in four countries were selected on the basis of their having in-situ turbidity sensor monitoring and water sampling data for TP to be used for calibration. We were aiming to find three years of data from each stream, preferably including a dry year, a wet year, and a hydrologically average year, but in this selection, we also favoured data series with the fewest possible data gaps. The cases represent a variety of catchment sizes, land use distributions, predominant soil types, turbidity ranges, and WFD environmental goals (Table 1\u003csup\u003e[1]\u003c/sup\u003e). The area-specific water discharge (over the long term and for the three selected years) is shown in Table 2. Further characteristics of the streams and their catchments are given in the supplementary material (Table S-VIII).\u0026nbsp;\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eTable 1\u003c/strong\u003e Case streams\u0026rsquo; catchment areas, main land uses, WFD river types, classification boundaries, and main soil types. Further stream and catchment characteristics are given in the supplementary material (Table S-VIII)\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"945\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eCountry\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003eStream name\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003eCatchment area\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003eLand use (%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eWFD river type\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"5\" valign=\"top\" style=\"width: 222px;\"\u003e\n \u003cp\u003eWFD environmental goals for TP (\u0026micro;g TP/l)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 251px;\"\u003e\n \u003cp\u003eMain soil types\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003ekm\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003eAgric\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003eForest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003eOther\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eAll are lowland rivers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eReference condition\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 32px;\"\u003e\n \u003cp\u003eHigh/ Good\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eGood/ Moderate\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003eMedian/ Poor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003ePoor/ Very Poor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 251px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eDK\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003eHorndrup\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e5.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eRCB-5\u003csup\u003e1\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 32px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e106\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 251px;\"\u003e\n \u003cp\u003eSandy loam (98.8%), Organic/Peat (1.2%)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eDK\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003eLyby-Gr\u0026oslash;nning\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e11.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eRCB-5\u003csup\u003e1\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 32px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e106\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 251px;\"\u003e\n \u003cp\u003eSandy loam (47%), Clayey loam (52%)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eFI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003eAurajoki\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e756\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eClay river, medium\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026lt;40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 32px;\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e130\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 251px;\"\u003e\n \u003cp\u003eMorain (54%), clay-rich (28%), organic/peat (11%)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eFI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003eHirvijoki\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e148\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eClay river, medium\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026lt;40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 32px;\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e130\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 251px;\"\u003e\n \u003cp\u003eClay (51%), Coarse sand with clay (25%), Gyttja/peat (10%), Coarse sand (6%), Fine sand (5%)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eFI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003eLeps\u0026auml;m\u0026auml;njoki\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eClay river, small\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026lt;40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 32px;\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e130\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 251px;\"\u003e\n \u003cp\u003eClay (63 %), Coarse sand with clay 9%, Gyttja/peat 8%\u003c/p\u003e\n \u003cp\u003eCoarse sand 6%, Fine sand with clay 6%, Fine sand 6%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eNO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003eM\u0026oslash;rdre\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e7.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eClay river, small\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 32px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 251px;\"\u003e\n \u003cp\u003eSilty clay (65%), ca. 35% morain in upstream parts\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eNO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003eSkuterud\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e4.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eClay river, small\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 32px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 251px;\"\u003e\n \u003cp\u003eSilty clay (60%), ca 40% morain in upstream parts\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003eH\u0026aring;ga\u0026aring;n\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e121\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eR-07\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 32px;\"\u003e\n \u003cp\u003e43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e101\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 251px;\"\u003e\n \u003cp\u003eMorain (33%), clay (23%) \u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003eSkivarp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e122\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eR-07\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 32px;\"\u003e\n \u003cp\u003e32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e112\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 251px;\"\u003e\n \u003cp\u003eClay (47%), sandy soils (27%)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 58px;\"\u003e\n \u003cp\u003eSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 94px;\"\u003e\n \u003cp\u003eS\u0026auml;vja\u0026aring;n\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e746\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 33px;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 143px;\"\u003e\n \u003cp\u003eR-07\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 32px;\"\u003e\n \u003cp\u003e38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 38px;\"\u003e\n \u003cp\u003e133\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 251px;\"\u003e\n \u003cp\u003eMorain (41%) clay (24 %)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003csup\u003e1\u003c/sup\u003e RCB-5: Lowland, Large, moderate-high alkalinity.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e2\u0026nbsp;\u003c/sup\u003eR-07: Lowland, \u0026lt; 10 000, organic and calcareous. (Lowland (\u0026lt; 200m) high alkaline (\u0026gt; 1 mekv/l) and humic (\u0026gt;30 mgPt/l).). May be transferred to a new typology class, Clay rivers, but this has not yet been done.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e3\u0026nbsp;\u003c/sup\u003eThe mean of a span of 68-136 \u0026micro;g TP/l. The boundary is based on Lyche Solheim et al. (2024) https://projects.au.dk/fileadmin/projects/nordbalt-ecosafe/Filer/D1_2_FactSheetsWithRefValuesAndGMboundaryValuesDraft.pdf since DK has not yet set class boundaries for streams.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e4\u003c/sup\u003e For larger streams, the soil type close to the monitoring station is given\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2\u003c/strong\u003e Average area-specific water discharge (l/s and km\u003csup\u003e2\u003c/sup\u003e) for the selected years and longer term means (LTM). Blue, green, and pink indicate the wettest, average, and driest of the three chosen years\u003c/p\u003e\n\u003ctable style=\"border-collapse: collapse;border: none;width: 596px;\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 23.9pt;border: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eC\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.45pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eName\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e2016\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e2017\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e2018\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e2019\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e2020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e2021\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e2022\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e2023\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 40.4pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eLTM\u003c/span\u003e\u003c/p\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.75pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eYears for LTM\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 23.9pt;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-left: 1pt solid windowtext;border-image: initial;border-top: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.45pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"9\" style=\"width: 289.2pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:.5in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;text-align:center;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e- l/s/km\u003csup\u003e2\u003c/sup\u003e -\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.75pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eFrom-to\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 23.9pt;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-left: 1pt solid windowtext;border-image: initial;border-top: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eDK\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.45pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eHorndrup\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#D9E2F3;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e10.0\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#E2EFD9;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e8.6\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#FBE4D5;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp 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style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eDK\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.45pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eLyby\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp 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style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e7.0\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#FBE4D5;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e3.6\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#E2EFD9;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp 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style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;\"\u003e5.2\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.75pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;\"\u003e1991-2020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 23.9pt;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-left: 1pt solid windowtext;border-image: initial;border-top: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eFi\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.45pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eAurajoki\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#FBE4D5;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e4.9\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#D9E2F3;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e\u0026nbsp;12.0\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp 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top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eFI\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.45pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;background:white;\"\u003eHirvijoki\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp 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style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;\"\u003e7.6\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.75pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;\"\u003e1991-2020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 23.9pt;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-left: 1pt solid windowtext;border-image: initial;border-top: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp 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style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;\"\u003e6.4\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.75pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;\"\u003e1991-2020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 23.9pt;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-left: 1pt solid windowtext;border-image: initial;border-top: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eSE\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.45pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003eS\u0026auml;vja\u0026aring;n\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 31.1pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;background: rgb(251, 228, 213);padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e2.6\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#E2EFD9;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e3.9\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cstrong\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;background:#D9E2F3;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e6.1\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width:31.1pt;border-top:none;border-left:none;border-bottom: solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0in 5.4pt 0in 5.4pt;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;font-family:Calibri;color:black;\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 40.4pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;\"\u003e7.6\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 66.75pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin-top:0in;margin-right:0in;margin-bottom:0in;margin-left:0in;font-size:11.0pt;font-family:\"Calibri\",sans-serif;line-height:normal;'\u003e\u003cspan style=\"font-size:13px;\"\u003e1991-2020\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eSensor equipment and sensor data quality control\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAn overview of the sensor brands used is given in the supplementary material (Table S-I). Data were quality-controlled by the respective institutes according to their standard procedures. This included a control to assess whether outliers could be explained by a rapid increase in water discharge or by pollution on the sensor lens. The respective institutes also assessed whether cleaning the lenses affected the data, usually seen as an abrupt change in turbidity after cleaning.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eMissing values were linearly interpolated using the R package \u0026lsquo;chillR function interpolate_gaps\u0026rsquo; (Luedeling, 2018). Missing values were interpolated if the number of consecutive gaps did not exceed 48, which equals two days of measurements. Longer gaps were not interpolated and were left as missing values.\u0026nbsp;\u003c/p\u003e\n\u003cp id=\"_Toc193384589\"\u003eWater sampling procedures and chemical analyses of TP for calibration\u003c/p\u003e\n\u003cp\u003eIn all the streams, a surrogate relationship equation between sensor turbidity and the TP water sample data have been calculated. TP samples were collected by hand, by automatic samplers, or by both. There were variations in the sampling strategies of the monitoring programmes (supplementary material, Table S-II), but all had at least 65 TP samples for calibration (supplementary material, Table S-III). In a comparison of 31 streams in Northern Europe, Skarb\u0026oslash;vik et al. (2023) found that at least 70 samples for calibration yielded an R\u003csup\u003e2\u003c/sup\u003e value above 0.6 between turbidity and SS.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe TP was analysed by accredited laboratories according to nationally approved standards (supplementary material, Table S-IV).\u003c/p\u003e\n\u003cp id=\"_Toc193384590\"\u003eData analyses and statistics\u003c/p\u003e\n\u003cp\u003eMimic data series were prepared for all streams\u0026nbsp;by extracting different frequency data from the hourly sensor turbidity data. We assumed monitoring regimes where sampling can occur randomly within the boundaries of a week, 14 days, or a month. In addition, we also assumed a more realistic sampling strategy, selecting Mondays\u0026ndash;Thursdays during working hours, due to the practical need to deliver samples to the laboratory by Thursday before closing hours. This resulted in the following six sampling strategies:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eusing all hours of the day every weekday and selecting (i) weekly, (ii) fortnightly, and (iii) monthly samples from this; and\u003c/li\u003e\n \u003cli\u003eusing only working hours (8:00\u0026ndash;15:00) from Monday to Thursday and selecting (iv) weekly, (v) fortnightly, and (vi) monthly sampling from this.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eFor each sampling strategy, 1,000 datasets were randomly constructed, and annual mean concentrations were calculated. These were then compared with annual mean concentrations based on hourly data from the sensors. This enabled us to calculate the percentage of uncertainty for each sampling strategy by using the ChillR package. Total uncertainty was then calculated as the root mean square error (RMSE) of prediction divided by the actual mean turbidity value from hourly observations (TrueTurb): RMSE/TrueTurb.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNext, we decided on a set of potential factors to explain any variation in total uncertainty between the streams. The factors were chosen based on typical information that is readily available. This included catchment size and land use, as well as area-specific discharge and flashiness of the flow. For the latter, the Richards-Baker flashiness Index (RBI; Baker et al., 2007) was calculated using the ContDataQC in R package (Leppo, 2022). In addition, we included three characteristics related to turbidity: standard deviation, proportion of outliers, and range. For range, the lower values for all streams were zero or near zero, and we hence tested for the maximum turbidity recorded and the 95 and 98 percentiles. Since the maximum turbidity in some cases can equal the maximum value that the sensor can record, and is often reached in only a few spikes that may have been caused by instrument error, we decided that using the 95 \u0026nbsp;and 98 percentiles would be more robust.\u003c/p\u003e\n\u003cp\u003eWe then fitted a linear model using the R program and checked this for multicollinearity by using variance inflation factors (VIF) and normality of residual distribution (Shapiro test and residual plots). Some of the parameters were log10-transformed to improve the visual representation in the graphs (area, discharge per unit area, and percentiles of turbidity). While the total dataset comprised 90 observations (10 rivers, 3 years, 3 sampling strategies \u0026ndash; here omitting the sampling only during working hours, see results\u0026rsquo; section), the model was developed using a randomly selected half (45 observations) and validated with the remaining half (45 observations). This we did four times to ensure that the random selection did not include outliers or other data that affected the results.\u003c/p\u003e\n\u003cp\u003eFor all the streams, the TP concentrations analysed from grab samples were used for calibration between turbidity and TP. No rule has been determined for how good such a correlation should be in order to use turbidity as a proxy for another substance. In this study, we both assessed the R\u003csup\u003e2\u003c/sup\u003e and scrutinized the correlation graphs (supplementary material) and decided that an R\u003csup\u003e2\u003c/sup\u003e of 0.6 or above gave an acceptable correlation. This issue is further deliberated upon in the discussion session, but it should be noted that most of the data analyses have been performed on turbidity alone, and not on the proxy.\u0026nbsp;\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eImportance of sampling strategy for calculating mean turbidity\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe variations in the mean annual turbidity for all 10 streams for (relatively) dry, average, and wet years are shown in the supplementary material (supplementary material, Figure S-II). The smallest and most extreme variations in turbidity values were found, respectively, in the dry year of 2018 in the Finnish river Aurajoki and in the wet year of 2020 in Denmark\u0026rsquo;s Horndrup Stream. The river Aurajoki\u0026rsquo;s range in mean annual turbidity was 13\u0026ndash;41 FNU (standard deviation of 3.6), whereas the Horndrup Stream had a range of 6\u0026ndash;133 FNU (standard deviation of 15). Figure 1 combines the total uncertainty of mean annual turbidity (y-axis) for all three years in the 10 streams based on the six sampling strategies (x-axis).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAs expected, the uncertainty in mean annual turbidity increased with decreased sampling frequency. There was a slight difference between sampling at any random hour and on weekdays and sampling during working hours on Monday to Thursday, as the median uncertainty was lower when the sampling was limited to working hours (Fig 1). This illustrates how the shorter the window of sampling opportunity, the lower the mean value may be, as more extreme events are likely to be missed. However, when compared to the differences between monthly, fortnightly, and weekly sampling, the differences between sampling on all days and at all hours of the day versus sampling only on four days a week during working hours were deemed negligible. For all streams in total, weekly sampling (on all days at all hours) gave a mean uncertainty of true mean turbidity of 17\u0026plusmn;9% (mean \u0026plusmn; standard deviation with a range of 4.5%-35% (max. and min.)), fortnightly sampling \u0026ndash; 26\u0026plusmn;13% (10% \u0026ndash; 51%) and monthly sampling 40\u0026plusmn;19% (16%\u0026ndash;85%).\u003c/p\u003e\n\u003cp\u003eUncertainty varied among the studied streams (Figure 2). The highest levels of uncertainty were found in the two Danish streams and the lowest were found in the three Finnish streams and the Swedish Haga\u0026aring;n.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThere was no clear connection between annual water discharge and the uncertainty of finding annual true mean turbidity, as shown for weekly sampling in Figure 3. Six of the streams had their highest level of uncertainty in the wettest year, whereas four streams had their highest level of uncertainty in years of either dry or average water discharge. However, in the Swedish Skivarp, there was little difference in water discharge between the wet and average years. The results indicate that, for some streams, the uncertainty of finding average annual concentrations can increase in years with high water discharge, but that most probably the distribution of water discharge throughout the year is also of importance. Our data material was not deemed sufficient to explore more detailed analyses of the hydrological impact on uncertainty beyond looking at the flashiness index, which also had a poor correlation with the uncertainty (Table 3).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFactors affecting uncertainty\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo evaluate which factors may cause the variation in uncertainty of the mean annual turbidity, we tested against a set of available, possible explanatory factors (Table 3, and supplementary material, Figure S-I). We found correlations between total uncertainty and land use percentage of agricultural (R\u003csup\u003e2\u003c/sup\u003e=0.43) or forested (R\u003csup\u003e2\u003c/sup\u003e=0.39) land, catchment size (R\u003csup\u003e2\u003c/sup\u003e=0.35), and sampling frequency (R\u003csup\u003e2\u003c/sup\u003e=0.31).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe then fitted these parameters into a multiple linear model to explore how the parameters together could predict total uncertainty. As noted above, the dataset of 90 observations was split in two, and the model was calibrated for 45 datasets and then tested on the remaining 45.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3\u003c/strong\u003e Relationship between the total uncertainty (of finding mean annual turbidity), and a set of available explanatory factors\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"604\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePossible explanatory factors (x in the equations in the next column). All were log10 transformed\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 180px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEquation (y is the total uncertainty; x is the tested explanatory factor)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 49px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 74px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ep\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eStats. Info\u003csup\u003e1\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003eNumber of samples per year (n)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 180px;\"\u003e\n \u003cp\u003ey=10^(x*-0.00935+1.64153)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 49px;\"\u003e\n \u003cp\u003e0.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 74px;\"\u003e\n \u003cp\u003e1.42E-08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eNND\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003eSize of catchment area (km\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 180px;\"\u003e\n \u003cp\u003ey=10^(x*-0.20221+1.70088)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 49px;\"\u003e\n \u003cp\u003e0.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 74px;\"\u003e\n \u003cp\u003e9.76E-10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eND\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003eProportion of agricultural area (%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 180px;\"\u003e\n \u003cp\u003ey=10^(x*0.00881+0.90449)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 49px;\"\u003e\n \u003cp\u003e0.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 74px;\"\u003e\n \u003cp\u003e1.63E-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eND\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003eProportion of forested area (%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 180px;\"\u003e\n \u003cp\u003ey=10^(x*-0.00788+1.65694)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 49px;\"\u003e\n \u003cp\u003e0.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 74px;\"\u003e\n \u003cp\u003e3.41E-11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eND\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003eDischarge per catchment area (l/s and km\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 180px;\"\u003e\n \u003cp\u003ey=10^(x*0.01506+1.3574)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 49px;\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 74px;\"\u003e\n \u003cp\u003e0.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eNS\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003eFlashiness index (RBI)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 180px;\"\u003e\n \u003cp\u003ey=10^(x*0.38044+1.24591)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 49px;\"\u003e\n \u003cp\u003e0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 74px;\"\u003e\n \u003cp\u003e1.25E-02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eND\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003eTurbidity 98-percentile (NTU/FNU)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 180px;\"\u003e\n \u003cp\u003ey=10^(x*0.26894+0.77781)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 49px;\"\u003e\n \u003cp\u003e0.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 74px;\"\u003e\n \u003cp\u003e6.65E-04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eND\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003eTurbidity maximum level (NTU/FNU)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 180px;\"\u003e\n \u003cp\u003ey=10^(x*0.33404+0.42717)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 49px;\"\u003e\n \u003cp\u003e0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 74px;\"\u003e\n \u003cp\u003e6.98E-07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eND\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 255px;\"\u003e\n \u003cp\u003eTurbidity 95-percentile (NTU/FNU)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 180px;\"\u003e\n \u003cp\u003ey=10^(x*0.16224+1.04445)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 49px;\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 74px;\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eNS\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003eRatio of turbidity outliers/number of samples\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 180px;\"\u003e\n \u003cp\u003ey=10^(x*0.45126+0.04556)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 49px;\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 74px;\"\u003e\n \u003cp\u003e7.45E-03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eND\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 255px;\"\u003e\n \u003cp\u003eThe standard deviation of turbidity (NTU/FNU)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 180px;\"\u003e\n \u003cp\u003ey=10^(x*0.34252+0.8062)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 49px;\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 74px;\"\u003e\n \u003cp\u003e1.07E-05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003eND\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003csup\u003e1\u003c/sup\u003eStatistical information: NND: Not normally distributed; ND: Normally distributed; NS: Not significant\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSome parameters were omitted due to having a similar nature or strong correlation with others (e.g. percentage of agriculture was negatively correlated with percentage of forest, the 95 and 98 percentiles of turbidity were correlated, and so on). The VIF scores of the parameters used were below 5 for all predictions, indicating no multicollinearity concern. The model included the following parameters:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003enumber of samples (n)\u0026nbsp;\u003c/li\u003e\n \u003cli\u003ecatchment size (Cz)\u0026nbsp;\u003c/li\u003e\n \u003cli\u003epercentage of agricultural area (A)\u003c/li\u003e\n \u003cli\u003edischarge per area (Qa)\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eflashiness of water discharge (RBI) \u0026nbsp;\u0026nbsp;\u003c/li\u003e\n \u003cli\u003e98 percentile of turbidity (T)\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe fitted regression of this uncertainty model is as follows:\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 482px;\"\u003e\n \u003cp\u003eU= 10^[1,3914 \u0026nbsp;- (0.0084 * n) \u0026ndash; (0.1019 * log10(Cz)) + (0.0052 * A) \u0026ndash; (0.0895 * log10(Qa)) + (0.0644 * log10(T))]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eEq. 1 (Model 1)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003ewhere U is the total uncertainty of finding true mean turbidity.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe model was significant, p\u0026lt;0.001, indicating that at least one of the predictors significantly affected the total uncertainty. The model explained 75% of the variance in the total uncertainty (adjusted R\u003csup\u003e2\u003c/sup\u003e=75). See supplementary material Table S-V for further details.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNext, we tested a much simpler model (Model 2), which includes only the parameters n, Cz, and A. These were chosen because they are easily available parameters and, moreover, the other parameters in Model 1 seemed less important (cf. p-values in Table 3). The simplified uncertainty model is expressed as:\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 482px;\"\u003e\n \u003cp\u003eU = 10^[1.3812 \u0026ndash; (0.0095 * n) \u0026ndash; (0.0003* Cz) + (0.0066* A)]\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 122px;\"\u003e\n \u003cp\u003eEq. 2 (Model 2)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe model was significant, p\u0026lt;0.001, indicating that at least one of the predictors significantly affected the total uncertainty. The model explained 79% of the variance in the total uncertainty (adjusted R\u003csup\u003e2\u003c/sup\u003e=79). See supplementary material Table S-VI for further details. Figure 4 shows the results of the tests for both models. \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBased on Equation 2, we simulated how uncertainty can change when the number of samples collected per year from the streams included in this study is increased (Figure 5a for catchment size and 5b for land use). Table 4 shows the number of samples per year that are needed to find a mean turbidity value with uncertainty less than 10%, 20%, and 40% respectively. In terms of land use, we have shown this for the proportion of agricultural land, but in the 10 studied catchments, the remaining land use was mostly forest (Table 1), which indicates that an increasing proportion of forest will reduce uncertainty. The table illustrates, for example, that larger rivers may be sampled less often than smaller streams within the same uncertainty, but at the same time, a large agricultural river may need the same number of samples as a smaller forested stream. A large river (800 km\u003csup\u003e2\u003c/sup\u003e catchment area) with only 20% agriculture could give a mean TP concentration within 10% uncertainty with 29 samples per year, whereas a small stream (5 km\u003csup\u003e2\u003c/sup\u003e catchment area) with 85% agriculture would need 100 samples to achieve the same level of uncertainty.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 4\u003c/strong\u003e The number of samples each year to keep within 10%, 20% and 40% uncertainty (U) of finding \u0026lsquo;true mean\u0026rsquo; concentration of turbidity, based on catchment area (Cz) and proportion of agricultural land (A). Empty cells: data from our study did not cover this range\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" style=\"width: 244px;\"\u003e\n \u003cp\u003eNo of samples a year to keep within a % of uncertainty (U)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eCz (km\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003eA (%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e10% U\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e20% U\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 74px;\"\u003e\n \u003cp\u003e40% U\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e800\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 74px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 74px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003e85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 74px;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 74px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 74px;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003e85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 74px;\"\u003e\n \u003cp\u003e31\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003e5\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 74px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 74px;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 79px;\"\u003e\n \u003cp\u003e85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 74px;\"\u003e\n \u003cp\u003e36\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eCorrelations and significance for phosphorus concentrations in streams\u003c/p\u003e\n\u003cp\u003eIn the above results, the data analyses are concerned with turbidity, as we wanted to assess the uncertainty in finding annual means independently of what turbidity may be a proxy for. However, turbidity is not used to evaluate the state of water bodies under the WFD. We therefore correlated turbidity with TP and found that three of the 10 streams had a correlation (R\u003csup\u003e2\u003c/sup\u003e) below 0.6 (supplementary material, Table S-V and Figure S-III) \u0026ndash; the Skivarp, Haga\u0026aring;n, and M\u0026oslash;rdre \u0026ndash; and these three streams have therefore been omitted from the following data analyses. The reasons for the poorer correlations may be linked to phosphorus from sources such as sewage or animal manure, but this issue will not be further explored in this work.\u003c/p\u003e\n\u003cp\u003eAn important question arising from the above data analyses is whether the annual mean TP concentration is more likely to be underestimated or overestimated. Hence, we have used the data for the seven streams with an acceptable TP\u0026ndash;turbidity correlation and estimated that, on average for 1,000 runs, there was a larger risk of underestimating the mean turbidity and, hence, the TP mean concentration. The proportion of runs where estimated mean turbidity was lower than the \u0026lsquo;real mean\u0026rsquo;, was, on average, 58% for weekly sampling, 60% for fortnightly sampling, and 65% for monthly sampling (Figure 6). From this, it follows that managers will most likely assume that the state of a river water body is in a better class than it is, based on a \u0026lsquo;true mean\u0026rsquo; of hourly sampling.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNext, we compared the calculated sensor-based annual means of TP with the environmental goals for all streams (Figure 7) for weekly and monthly sampling strategies. For monthly sampling, the span between the lowest and highest annual mean TP concentrations varied from 86 \u0026micro;g/l in the Swedish S\u0026auml;vja\u0026aring;n to 978 \u0026micro;g/l in the Danish Lyby, and the average for all streams was ca. 300 \u0026micro;g/l. Weekly sampling gave a span of 6 \u0026micro;g/l for S\u0026auml;vja\u0026aring;n, 350 \u0026micro;g/l for Lyby, and an average range of 117 \u0026micro;g/l for all streams. In some of the streams, the lowest mean sensor-based TP concentration was higher than the environmental goal. This included Aurajoki and Skuterud for both the weekly and monthly sampling strategies, and Lyby, Hirvijoki, and Leps\u0026auml;m\u0026auml;njoki for the weekly sampling strategy. This means that whatever sampling strategy is used for the three years with different hydrological conditions, the annual mean concentration of TP would show the stream as having a moderate or worse status. For the other streams, the lowest and highest estimates of the mean TP concentrations could fall below, above, or close to the environmental goal.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eAlthough the WFD was agreed by EU member states 25 years ago (in 2000 in the EU and in 2006 in Norway), there are still issues to be further explored related to its cost-effective implementation (Carvalho et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Lyche-Solheim et al., 2025). The economic costs of implementing the WFD may become an increasing challenge in a world facing uncertain economic developments due to ongoing military conflicts and potential trade wars, and a subsequent need to intensify food production locally. Moreover, eutrophication is a challenge that can be expected to increase in magnitude in the years to come due to climate change (Kosten et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Jeppesen et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Solheim et al., 2025). Hence, it will be of great importance to choose the most cost-effective monitoring strategy to ensure that streams under the WFD are properly managed.\u003c/p\u003e \u003cp\u003eIn this study, our main concern has been to assess the uncertainty of using the mean concentration of TP as an indicator of ecological status in streams. Achieving accurate estimates of TP concentrations in streams is also of great importance for the ecological quality of lakes as riverine inputs often determines the in-lake concentration (Jensen et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). In our study of 10 Nordic streams, we found that the average mean turbidity, which is a parameter that correlates both with TP and other particle-associated substances, will depend on several factors, for which we extracted three explanatory variables that are easily available and can therefore provide a basis for planning cost-effective monitoring strategies by managers: catchment size, catchment land use, and the number of samples collected per year. Importantly for managers, we found that larger streams can be sampled less often than smaller streams within the same uncertainty, but at the same time, a large agricultural river may need the same number of samples as a smaller forested stream. Our model is based on a series of assumptions that are discussed further below.\u003c/p\u003e \u003cp\u003eOur model indicates that larger streams tend to have less temporal variation in turbidity and, therefore, also in concentrations of particle-associated substances than do smaller streams, which often respond more rapidly to rain or snow melt events, with ensuing increases in water flow. Similar results were found by Coynel et al. (2004) when comparing the uncertainty of flux estimates of suspended particulate matter. They concluded that to find SS fluxes within 20% uncertainty, the large river Garonne would need to be sampled every third day, whereas a smaller river would have to be sampled as often as every seventh hour.\u003c/p\u003e \u003cp\u003eOur model also indicates that the uncertainty of a mean annual concentration is higher in agricultural catchments than in catchments dominated by forest cover. De Wit et al. (2020) documented that observed TP concentrations in Nordic agricultural streams were much higher than in forested and natural catchments. As discussed by Skarb\u0026oslash;vik et al. (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), the soil types in Nordic catchments dominated by agriculture are likely to be more fine-grained than in catchments dominated by forest, and that seasonal changes in vegetation cover leave the soil more vulnerable to erosion. There may also be fewer trees along the riverbanks and therefore more bank erosion in agricultural areas (Beeson \u0026amp; Doyle, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; Abernethy \u0026amp; Rutherfurd, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). This, again, can result in higher concentrations and thereby greater variations in the concentrations of particulate matter and TP, thereby making it more difficult to find the true mean concentration.\u003c/p\u003e \u003cp\u003eThe use of the model in other stream types needs to be tested on new datasets, but as we have based our model on 10 streams of differing size and land use, we expect our model to be relatively robust, at least for streams with characteristics similar to those of our Nordic streams (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e2\u003c/span\u003e, and Table S-VIII in supplementary material).\u003c/p\u003e \u003cp\u003eThe implications of our findings for managers following up the WFD include designing monitoring strategies based on catchment size and land use. However, as also noted by Skeffington et al. (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), the need for accurate estimates of the status of the water body may increase as the water quality approaches the environmental goal. In streams where the environmental goal will not be reached regardless of sampling strategy (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e), fine-tuning to find a less uncertain annual mean TP concentration may not be the most sensible use of funds and a better strategy may be to use available funds to reduce the loss of phosphorus and sediments to the water environment. On the other hand, a less accurate monitoring strategy would make it more difficult to track whether implemented measures work as planned.\u003c/p\u003e \u003cp\u003eAnother question is how these findings may affect the many biological indices that are based on annual mean TP concentrations. We have shown that the mean turbidity value found from monthly, fortnightly, and even weekly sampling in streams will most likely, in about 60% of the runs, be lower than the \u0026lsquo;true mean\u0026rsquo; (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e). This also implies that the indices developed between TP and biological indicators are probably calibrated with TP concentrations that are too low, since the biological indicators are based on monitoring programmes that usually use intervals far less frequent than hourly intervals (e.g. Schneider \u0026amp; Skarb\u0026oslash;vik, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). On the other hand, our true mean includes all of a year\u0026rsquo;s peak values that have been detected at hourly intervals. Certainly, for both hazardous substances and the calculation of loads of all substances, the identification of maximum concentrations will be important. But does it follow that the same is true for the mean concentration of nutrients? In other words, will a shorter period of high concentrations of nutrients seriously affect biota, or is the \u0026lsquo;true mean\u0026rsquo;, in terms of effect on biological indicators, more related to the TP concentrations outside of the peaks? This is a question worth pursuing in forthcoming studies.\u003c/p\u003e \u003cp\u003eThe source of errors in the data used in this study relates mainly to the reliability of the sensors used and to the relationship between turbidity and proxies (here: TP concentration). Kahiluoto et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) found that turbidity sensor measurement had an uncertainty of 11\u0026ndash;27% (k\u0026thinsp;=\u0026thinsp;2) for the range of 5\u0026ndash;40 FNU. Skarb\u0026oslash;vik et al. (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) discussed how different sensor brands may give different slopes of the correlation between SPM and turbidity by sensors, but they also found that this could be related to the type of filter used when analysing SPM. As far as we know, there is no set rule for how good a correlation should be in order to use turbidity as a proxy for another substance. Lannerg\u0026aring;rd et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) presented an overview of the R\u003csup\u003e2\u003c/sup\u003es between TP and turbidity from eight different studies, varying from 0.25 to 0.90, but where most of the correlations had an R\u003csup\u003e2\u003c/sup\u003e above 0.6. Minaudo et al. (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) have shown that a nonlinear model between turbidity and TP can sometimes be more feasible than a linear regression model. Moreover, K\u0026auml;m\u0026auml;ri et al. (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) studied the correlations between turbidity from sensors and TP from grab samples in three Finnish streams. The R\u003csup\u003e2\u003c/sup\u003e values of the linear calibration varied between 0.77 and 0.80, but if a few high TP concentrations were omitted, the R\u003csup\u003e2\u003c/sup\u003e was reduced to 0.57\u0026ndash;0.74. This illustrates that R\u003csup\u003e2\u003c/sup\u003e alone is insufficient evidence for correlations, and that consideration should be given to correlation graphs to check for single high values, as well as to other statistics. In our case, this was achieved through the graphs shown in the supplementary material, Figure S-III, and when analysing impacts of sampling frequency on TP annual means, we only used the rivers with an R\u003csup\u003e2\u003c/sup\u003e between turbidity and TP above 0.65.\u003c/p\u003e \u003cp\u003eOur study has shown that stream water quality monitoring programmes with infrequent sampling run a high risk of obtaining unreliable mean concentrations. McDowell et al. (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) noted that in a river monitoring network in New Zealand with monthly sampling, costs would have to increase by 5.3 times to reach statistically acceptable results within a 5-year period. They therefore concluded that it might be necessary to increase monitoring investments in order to demonstrate policy results for water quality improvement. Moreover, as stated by the EC (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2003\u003c/span\u003e):\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eThe cost of measures for improvement in water status would be orders of magnitude greater than the costs of monitoring. The extra costs of monitoring to reduce the risk of misclassification might therefore be justified in terms of ensuring that decisions to spend larger sums of money required for improvements are based on reliable information on status.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eNevertheless, in practice there will often be a trade-off between costs for monitoring and costs for measures, and the distance between the environmental goal and the current state of a water body may offer guidance on how detailed a monitoring programme should be. For water bodies that are in a very poor state, monitoring could perhaps be geared towards finding the main pollutant sources and funding might best be used to reduce the impact of these.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThe uncertainty in annual mean turbidity and TP concentrations increased with decreased sampling frequency in 10 Nordic streams. Weekly samples gave the lowest uncertainty, whereas uncertainty increased with fortnightly and monthly sampling. Uncertainty varied with stream and catchment properties, but for all streams there was a higher risk of underestimating the mean TP than of overestimating it. This means that there is a risk that managers will believe their water bodies are in a better state than they actually are. In our simpler model, the variation in uncertainty was explained by catchment size and land use in the catchment. We found that large streams may be sampled less often than smaller streams, but at the same time, a large agricultural river may need the same number of samples as a smaller forested stream. A large river with a catchment area of about 800 km\u003csup\u003e2\u003c/sup\u003e and with only 20% agriculture could give a mean TP concentration within 10% uncertainty with 29 samples per year, whereas a small stream with a catchment area of 5 km\u003csup\u003e2\u003c/sup\u003e and 85% agriculture would require 100 samples a year to achieve the same level of uncertainty. By using our model, managers could direct their monitoring programmes towards the optimal sampling frequency for rivers of different catchment size and land use. At the same time, they might look at the distance between the environmental goal and the current status, as funding could be better spent on reducing nutrient losses if the water bodies are in a particularly poor state.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAll authors have read, understood, and have complied as applicable with the statement on \u0026ldquo;Ethical responsibilities of Authors\u0026rdquo; as found in the Instructions for Authors.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eFunding declaration\u003c/strong\u003e: This paper was funded by the EU Horizon project NORDBALT-ECOSAFE (Grant Agreement No. 101060020). The Danish work was also funded by Innovation Fund Denmark from the Industrial Researcher programme for the project \u0026lsquo;SENTEM\u0026rsquo; at Envidan and Aarhus University, Denmark (Grant Agreement No. 0153-44 00078B). The Finnish data was funded by the Centre for Southwest Finland Economic Development, Transport and the Environment (sensor data from the Aurajoki River) and The Water Protection Association of The River Vantaa (sensor data from the River Leps\u0026auml;m\u0026auml;njoki). Parts of the Finnish work has also been funded by the Flagship Program granted by the Research Council of Finland for Digital Waters Flagship (decision no. 359250). The Norwegian data were supported by the Biowater Centre of Excellence, funded by NordForsk under Project No. 82263, and the Norwegian Research Council under Contract No. 342631/L10, as well as from the JOVA Program, funded by the Norwegian Ministry of Agriculture and Food. The Swedish data was funded by the Swedish Agency for Marine and Water Management and by the EU-Life IP project Rich Waters.\u0026nbsp;\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eE.S. wrote the main manuscript text and had the idea for the paper. A.I. prepared many of the figures and tables, performed the statistical analyses and contributed with text.M.K., P.V., S.G.M.vV, E.E.L., J.F. contributed with data, inputs to the tables, ideas, and text. B.K. contributed with text, ideas and advice.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAbernethy, B \u0026amp; Rutherfurd, I.D. 2000. The effect of riparian tree roots on the mass-stability of riverbanks. \u003cem\u003eEarth Surface Processes and Landforms\u003c/em\u003e 25, 921\u0026ndash; 937. DOI:10.1002/1096-9837(200008)25:9\u0026lt;921::AID-ESP93\u0026gt;3.0.CO;2-7\u003c/li\u003e\n\u003cli\u003eAxe, P., Sonesten, L., Skarb\u0026oslash;vik, E., Leujak, W. \u0026amp; Nielsen, L., 2022. \u003cem\u003eInputs of Nutrients to the OSPAR Maritime \u003c/em\u003e\u003cem\u003eArea\u003c/em\u003e. In OSPAR, 2023: The 2023 Quality Status Report for the North-East Atlantic. 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Load estimation methodologies for British rivers and their relevance to the LOIS RACS(R) programme. \u003cem\u003eScience of the Total Environment\u003c/em\u003e 194-195, 379-389. https://doi.org/10.1016/S0048-9697(96)05377-6\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Footnotes","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e Please note that Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e1\u003c/span\u003e can be found at the very end of this manuscript.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Water quality, streams, turbidity, sensor, phosphorus, uncertainty","lastPublishedDoi":"10.21203/rs.3.rs-6436252/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6436252/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe annual mean concentration of nutrients is a commonly used parameter in implementing the Water Framework Directive, to assess current environmental status and distance from the environmental goal. However, the concentration of nutrients in streams may vary significantly over short time spans so finding the \u0026lsquo;true mean\u0026rsquo; concentration can be difficult. We used hourly turbidity data from optical sensors in 10 streams in four Nordic countries, and we prepared mimic data series for weekly, fortnightly, and monthly sampling strategies. We calibrated the sensor turbidity data with the total phosphorus data from grab samples. We then assessed how the annual mean values of both turbidity and phosphorus can vary, depending not only on the number of samples collected per year but also on stream and catchment characteristics. We found that the uncertainty of the annual mean concentration of total phosphorus decreased with increasing sampling frequency and increasing catchment size, and with a decreasing proportion of agricultural land in the catchment. We also found that there was a higher risk of underestimating the mean TP than of overestimating it, meaning that managers will assume that water quality is better than it is. Our work has resulted in an initial model that calculates the number of samples needed to achieve a given uncertainty in annual mean TP concentration for streams of varying catchment size and land use.\u003c/p\u003e","manuscriptTitle":"Using optical sensors to assess the impact of infrequent sampling on the uncertainty of stream annual mean turbidity and total phosphorus concentrations, and how this can affect the water quality status ","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-14 12:21:15","doi":"10.21203/rs.3.rs-6436252/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b42f9753-d038-4e3c-a25b-7d7903cab05a","owner":[],"postedDate":"May 14th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-06-19T14:09:05+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-14 12:21:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6436252","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6436252","identity":"rs-6436252","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}